Computational Role of Multiqubit Tunneling in a Quantum Annealer
Sergio Boixo, Vadim N. Smelyanskiy, Alireza Shabani, Sergei V. Isakov, Mark Dykman, Vasil S. Denchev, Mohammad Amin, Anatoly Smirnov, Masoud Mohseni, Hartmut Neven
备注：
Complete rewrite, much shorter version of arXiv:1411.4036. 7 pages, 7 figures
Quantum tunneling, a phenomenon in which a quantum state traverses energy barriers above the energy of the state itself, has been hypothesized as an advantageous physical resource for optimization. Here we show that multiqubit tunneling plays a computational role in a currently available, albeit noisy, programmable quantum annealer. We develop a non-perturbative theory of open quantum dynamics under realistic noise characteristics predicting the rate of many-body dissipative quantum tunneling. We devise a computational primitive with 16 qubits where quantum evolutions enable tunneling to the global minimum while the corresponding classical paths are trapped in a false minimum. Furthermore, we experimentally demonstrate that quantum tunneling can outperform thermal hopping along classical paths for problems with up to 200 qubits containing the computational primitive. Our results indicate that many-body quantum phenomena could be used for finding better solutions to hard optimization problems.
Quantum tunneling is a phenomenon in which a quantum state traverses energy barriers above the energy of the state itself. Tunneling has been hypothesized as an advantageous physical resource for optimization. Here we present the first experimental evidence of a computational role of multiqubit quantum tunneling in the evolution of a programmable quantum annealer. We develop a theoretical model based on a NIBA Quantum Master Equation to describe the multiqubit dissipative tunneling effects under the complex noise characteristics of such quantum devices. We start by considering a computational …
Experimental Measurement and Theoretical Analysis of Energy Relaxation Rates of an Interacting Two-Qubit System on a D-Wave Quantum Annealer
Tokyo University of Science（东京科学大学）；RIKEN（理化学研究所）；Department of Electrical, Electronic, and Communication Engineering, Faculty of Science and Engineering, Chuo University（中央大学理工学部电气电子通信工程系）
Quantum annealing (QA) has been proposed as a quantum enhanced optimization heuristic exploiting tunneling. Here, we demonstrate how finite range tunneling can provide considerable computational advantage. For a crafted problem designed to have tall and narrow energy barriers separating local minima, the D-Wave 2X quantum annealer achieves significant runtime advantages relative to Simulated Annealing (SA). For instances with 945 variables, this results in a time-to-99%-success-probability that is $\sim 10^8$ times faster than SA running on a single processor core. We also compared physical QA…
Quantum tunneling is a valuable resource exploited by quantum annealers to solve complex optimization problems. Tunneling events also occur during projective quantum Monte Carlo (PQMC) simulations, and in a class of problems characterized by a double-well energy landscape their rate was found to scale linearly with the first energy gap, i.e., even more favorably than in physical quantum annealers, where the rate scales with the gap squared. Here we investigate how a guiding wave function --- which is essential to make many-body PQMC simulations computationally feasible --- affects the tunnelin…
With progress in quantum technology more sophisticated quantum annealing devices are becoming available. While they offer new possibilities for solving optimization problems, their true potential is still an open question. As the optimal design of adiabatic algorithms plays an important role in their assessment, we illustrate the aspects and challenges to consider when implementing optimization problems on quantum annealing hardware based on the example of the traveling salesman problem (TSP). We demonstrate that tunneling between local minima can be exponentially suppressed if the quantum dyn…
The tunneling between the two ground states of an Ising ferromagnet is a typical example of many-body tunneling processes between two local minima, as they occur during quantum annealing. Performing quantum Monte Carlo (QMC) simulations we find that the QMC tunneling rate displays the same scaling with system size, as the rate of incoherent tunneling. The scaling in both cases is $O(Δ^2)$, where $Δ$ is the tunneling splitting. An important consequence is that QMC simulations can be used to predict the performance of a quantum annealer for tunneling through a barrier. Furthermore, by using open…
Bocconi University（博科尼大学）；Istituto Nazionale di Fisica Nucleare（意大利国家核物理研究所）；International Centre for Theoretical Physics（国际理论物理中心）
Quantum annealers aim at solving non-convex optimization problems by exploiting cooperative tunneling effects to escape local minima. The underlying idea consists in designing a classical energy function whose ground states are the sought optimal solutions of the original optimization problem and add a controllable quantum transverse field to generate tunneling processes. A key challenge is to identify classes of non-convex optimization problems for which quantum annealing remains efficient while thermal annealing fails. We show that this happens for a wide class of problems which are central …
In simple ferromagnetic quantum Ising models characterized by an effective double-well energy landscape the characteristic tunneling time of path-integral Monte Carlo (PIMC) simulations has been shown to scale as the incoherent quantum-tunneling time, i.e., as $1/Δ^2$, where $Δ$ is the tunneling gap. Since incoherent quantum tunneling is employed by quantum annealers (QAs) to solve optimization problems, this result suggests there is no quantum advantage in using QAs w.r.t. quantum Monte Carlo (QMC) simulations. A counterexample is the recently introduced shamrock model, where topological obst…
Quantum annealing is an optimization technique which potentially leverages quantum tunneling to enhance computational performance. Existing quantum annealers use superconducting flux qubits with short coherence times, limited primarily by the use of large persistent currents $I_\mathrm{p}$. Here, we examine an alternative approach, using qubits with smaller $I_\mathrm{p}$ and longer coherence times. We demonstrate tunable coupling, a basic building block for quantum annealing, between two flux qubits with small ($\sim 50~\mathrm{nA}$) persistent currents. Furthermore, we characterize qubit coh…
To date, a conclusive detection of quantum speedup remains elusive. Recently, a team by Google Inc.~[V.~S.~Denchev {\em et al}., Phys.~Rev.~X {\bf 6}, 031015 (2016)] proposed a weak-strong cluster model tailored to have tall and narrow energy barriers separating local minima, with the aim to highlight the value of finite-range tunneling. More precisely, results from quantum Monte Carlo simulations, as well as the D-Wave 2X quantum annealer scale considerably better than state-of-the-art simulated annealing simulations. Moreover, the D-Wave 2X quantum annealer is $\sim 10^8$ times faster than s…
Quantum phenomena have the potential to speed up the solution of hard optimization problems. For example quantum annealing, based on the quantum tunneling effect, has recently been shown to scale exponentially better with system size as compared with classical simulated annealing. However, current realizations of quantum annealers with superconducting qubits face two major challenges. First, the connectivity between the qubits is limited, excluding many optimization problems from a direct implementation. Second, decoherence degrades the success probability of the optimization. We address both …
For e-commerce websites, deciding the manner in which items are listed on webpages is an important issue because it can dramatically affect item sales. One of the simplest strategies of listing items to improve the overall sales is to do so in a descending order of sales or sales numbers. However, in lists generated using this strategy, items with high similarity are often placed consecutively. In other words, the generated item list might be biased toward a specific preference. Therefore, this study employs penalties for items with high similarity being placed next to each other in the list a…
